Phenolic acids comprise a class of phytochemical compounds that can be extracted from various plant sources and are well known for their antioxidant and anti-inflammatory properties. A few of the most common naturally occurring phenolic acids (i.e., caffeic, carnosic, ferulic, gallic, p-coumaric, rosmarinic, vanillic) have been identified as ingredients of edible botanicals (thyme, oregano, rosemary, sage, mint, etc.). Over the last decade, clinical research has focused on a number of in vitro (in human cells) and in vivo (animal) studies aimed at exploring the health protective effects of phenolic acids against the most severe human diseases. In this review paper, the authors first report on the main structural features of phenolic acids, their most important natural sources and their extraction techniques. Subsequently, the main target of this analysis is to provide an overview of the most recent clinical studies on phenolic acids that investigate their health effects against a range of severe pathologic conditions (e.g., cancer, cardiovascular diseases, hepatotoxicity, neurotoxicity, and viral infections—including coronaviruses-based ones).